2(11+w)(w-5)=72

Solution for 2(11+w)(w-5)=72 equation:

Simplifying
2(11 + w)(w + -5) = 72

Reorder the terms:
2(11 + w)(-5 + w) = 72

Multiply (11 + w) * (-5 + w)
2(11(-5 + w) + w(-5 + w)) = 72
2((-5 * 11 + w * 11) + w(-5 + w)) = 72
2((-55 + 11w) + w(-5 + w)) = 72
2(-55 + 11w + (-5 * w + w * w)) = 72
2(-55 + 11w + (-5w + w2)) = 72

Combine like terms: 11w + -5w = 6w
2(-55 + 6w + w2) = 72
(-55 * 2 + 6w * 2 + w2 * 2) = 72
(-110 + 12w + 2w2) = 72

Solving
-110 + 12w + 2w2 = 72

Solving for variable 'w'.

Reorder the terms:
-110 + -72 + 12w + 2w2 = 72 + -72

Combine like terms: -110 + -72 = -182
-182 + 12w + 2w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-182 + 12w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + 6w + w2) = 0

Factor a trinomial.
2((-13 + -1w)(7 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -1w)' equal to zero and attempt to solve:

Simplifying
-13 + -1w = 0

Solving
-13 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '13' to each side of the equation.
-13 + 13 + -1w = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1w = 0 + 13
-1w = 0 + 13

Combine like terms: 0 + 13 = 13
-1w = 13

Divide each side by '-1'.
w = -13

Simplifying
w = -13
Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {-13, 7}